The present invention relates to energy delivery devices, and more particularly, to techniques for evaluating transient characteristics of an energy delivery device to determine its state of charge.
To determine the state of charge (SOC) of an energy delivery device (e.g., a cell or a battery), one typically measures the open-circuit voltage (OCV; i.e., thermodynamic voltage of the cell at rest) and compares the OCV to a previously measured relationship between the OCV and state of charge. FIG. 1, an example of such a profile, shows the cell voltage measured 1.5 hours after interrupting a C/10-rate current that had been applied for 30 minutes. The figure shows data measured following a discharge (lower curve 102) and following a charge (upper curve 104); the two curves may differ because of hysteresis intrinsic to the cell chemistry. However, it can take a long time (over an hour) for a battery to relax to true open-circuit voltage after the current is turned off. In many cases, one wants to take advantage of short rest periods, on the order of a few minutes, to determine the state of charge of the battery.
Existing battery modeling literature describes the general nature of the voltage profile during relaxation. The voltage relaxes because of relaxing of concentration gradients by diffusion formed in the electrolyte and active electrode materials during passage of current. See, for example, papers by Chapman and Newman, AIChE J. 1973 p. 343 vol. 19 and Fuller, Doyle, and Newman, J. Electrochem. Soc., 1994, p. 982. These papers describe the theory that shows that, at sufficiently long times after interruption of current, the voltage profile will follow an exponential decay profile.
Voltage monitoring is used to determine state of charge. However, most published algorithms use a voltage measurement at a single point in time, and assume that the voltage is equal to the OCV. Alternatively, the algorithms use an equivalent circuit model of a cell to model capacitive and/or diffusive voltage transients.
If the rest period is not long enough to allow the cell to reach true OCV, then a single-point measurement will have error. Battery behavior is complex and difficult to match precisely with a simple equivalent-circuit model. A more sophisticated battery model can be used to predict battery behavior more accurately, but such models introduce a significant computational cost.